is a clockwise angle measured from due North. This is a problem, because all of the trigonometric functions are referenced to a counterclockwise angle measured from East.
A bearing of 34∘ corresponds to a trigonometric angle of θ1=90∘−34∘=56∘
The (x,y) values for the position of the ship after completing its first heading are:
x=(10.4mi)cos(56∘)
y=(10.4mi)sin(56∘)
The trigonometric angle for the second heading is θ2=90∘−90∘=0∘
The (x,y) values for the position of the ship after completing its second heading is:
x=(10.4mi)cos(56∘)+(4.6mi)cos(0∘)≈10.4mi
y=(10.4mi)sin(56∘)+(4.6mi)sin(0∘)≈8.6mi
The distance from port is:
d=√(10.4)2+(8.6)2≈13.5mi
Its trigonometric angle is:
θ=tan−1(yx)
θ=tan−1(8.610.4)
θ≈39.6∘
The bearing angle is:
θb=90∘−39.6∘=50.4∘
